On the validity of the LAD and LL classical radiation-reaction equations

The search of the correct equation of motion for a classical charged particle under the action of its electromagnetic (EM) self-field, the so-called \textit{radiation-reaction equation of motion}, remains elusive to date. In this paper we intend to point out why this is so. The discussion is based on the direct construction of the EM self-potentials produced by a charged spherical particle under the action of an external EM force. In particular we intend to analyze basic features of the LAD (Lorentz-Abraham-Dirac) and the LL (Landau-Lifschitz) equations. Both are shown to lead to incorrect or incomplete results.